There is a major difference in between heating wire and fuse wire
Heating wire has a very high melting point so it can be heated to very high temperature and due to its nature it withstand the temperature and does not melt. They are made up of high melting substance like nichrome.
Fuse has a very low melting point so it cannot be heated to very high temperature and due to its nature it cannot withstand the temperature and get melted easily. When used it melts when the current exceeds a certain limit. That is why it is used a protective aid. Made up of Magnesium etc.
So the correct answer is
the coil inside the heater may melt and break.